Abstract
We present a simple parallel algorithm for the single-source shortest path problem in planar digraphs with nonnegative real edge weights. The algorithm runs on the EREW PRAM model of parallel computation in O((n 2ε + n 1−ε) log n) time, performing O(n 2+ε log n) work for any 0<ε<1/2. The strength of the algorithm is its simplicity, making it easy to implement, and presumably quite efficient in practice. The algorithm improves upon the work of all previous algorithms. The work can be further reduced to O(n 2+ε, by plugging in a less practical, sequential planar shortest path algorithm. Our algorithm is based on a region decomposition of the input graph, and uses a well-known parallel implementation of Dijkstra's algorithm.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This work was partially supported by the EU ESPRIT LTR Project No. 20244 (ALCOM-IT), and by the DFG project SFB 124-D6 (VLSI Entwurfsmethoden und Parallelität).
Preview
Unable to display preview. Download preview PDF.
References
R. Ahuja, T. Magnanti, and J. Orlin, Network Flows, Prentice-Hall, 1993.
E. Cohen, Efficient parallel shortest-paths in digraphs with a separator decomposition, Proc. 5th Symp. on Par. Alg. and Archit. (SPAA), pp.57–67, 1993.
J. Driscoll, H. Gabow, R. Shrairman, and R.E. Tarjan, Relaxed heaps: An alternative to Fibonacci heaps with applications to parallel computation, Comm. of the ACM, 31(11):1343–1354, 1988.
G. Frederickson, Fast algorithms for shortest paths in planar graphs with applications, SIAM Journal of Computing, 16(6):1004–1022, 1987.
M. Fredman and R.E. Tarjan, Fibonacci heaps and their uses in improved network optimization algorithms, Journal of the ACM, 34(3):596–615, 1987.
H. Gazit and G. Miller, An O(√n log(n)) optimal parallel algorithm for a separator for planar graphs, Unpublished manuscript, 1987.
J. JáJá, An Introduction to Parallel Algorithms, Addison-Wesley, 1992.
C. Keßler and J. Träff, A library of basic PRAM algorithms and its implementation in FORK, Proc. 8th Symp. on Par. Alg. and Archit. (SPAA), to appear, 1996.
P. Klein, S. Rao, M. Rauch, and S. Subramanian, Faster shortest-path algorithms for planar graphs, Proc. 26th Symp. on Theory of Comp. (STOC), pp.27–37, 1994.
P. Klein and J. Reif, An efficient parallel algorithm for planarity, Journal of Computer and System Sciences, 37:190–246, 1988.
P. Klein and S. Subramanian, A linear-processor, polylog-time algorithm for shortest paths in planar graphs, Proc. 34th Symp. on Foundations of Computer Sc. (FOCS), pp.259–270, 1993.
R. Lipton and R.E. Tarjan, A separator theorem for planar graphs, SIAM Journal on Applied Mathematics, 36(2):177–189, 1979.
G. Miller, Finding small simple cycle separators for 2-connected planar graphs, Journal of Computer and System Sciences, 32:265–279, 1986.
V. Ramachandran and J. Reif, Planarity testing in parallel, Journal of Computer and System Sciences, 49(3):517–561, 1994.
J.L. Träff and C.D. Zaroliagis, A simple parallel algorithm for the single-source shortest path problem on planar digraphs, Tech. Rep. MPI-I-96-1-012, Max-Planck-Institut für Informatik, Saarbrcken, June 1996.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Träff, J.L., Zaroliagis, C.D. (1996). A simple parallel algorithm for the single-source shortest path problem on planar digraphs. In: Ferreira, A., Rolim, J., Saad, Y., Yang, T. (eds) Parallel Algorithms for Irregularly Structured Problems. IRREGULAR 1996. Lecture Notes in Computer Science, vol 1117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030108
Download citation
DOI: https://doi.org/10.1007/BFb0030108
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61549-1
Online ISBN: 978-3-540-68808-2
eBook Packages: Springer Book Archive